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Positive Solutions for a Hadamard Fractional p -Laplacian Three-Point Boundary Value Problem

Author

Listed:
  • Jiqiang Jiang

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Donal O’Regan

    (School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 TK33 Galway, Ireland)

  • Jiafa Xu

    (School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China)

  • Yujun Cui

    (State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

This article is to study a three-point boundary value problem of Hadamard fractional p -Laplacian differential equation. When our nonlinearity grows ( p − 1 ) -superlinearly and ( p − 1 ) -sublinearly, the existence of positive solutions is obtained via fixed point index. Moreover, using an increasing operator fixed-point theorem, the uniqueness of positive solutions and uniform convergence sequences are also established.

Suggested Citation

  • Jiqiang Jiang & Donal O’Regan & Jiafa Xu & Yujun Cui, 2019. "Positive Solutions for a Hadamard Fractional p -Laplacian Three-Point Boundary Value Problem," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:439-:d:232221
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    References listed on IDEAS

    as
    1. Abbas, Saïd & Benchohra, Mouffak & Lazreg, Jamal-Eddine & Zhou, Yong, 2017. "A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 47-71.
    2. Wenjie Ma & Shuman Meng & Yujun Cui, 2018. "Resonant Integral Boundary Value Problems for Caputo Fractional Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, August.
    3. Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
    4. Pei, Ke & Wang, Guotao & Sun, Yanyan, 2017. "Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 158-168.
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    Cited by:

    1. Jiafa Xu & Jiqiang Jiang & Donal O’Regan, 2020. "Positive Solutions for a Class of p -Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems," Mathematics, MDPI, vol. 8(3), pages 1-13, February.
    2. Binlin Zhang & Rafia Majeed & Mehboob Alam, 2022. "On Fractional Langevin Equations with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.

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